Application Note, V 1.1, July 2006
M O S F ET P o w e r L o s s e s
Calculation Using the DataSheet Parameters
by Dr. Dušan Graovac, Marco Pürschel,
Andreas Kiep
Automotive Power
N e v e r
s t o p
t h i n k i n g .
MOSFET Converter Losses
Table of Content
1
Abstract..........................................................................................................................................3
2
2.1
2.1.1
2.2
2.2.1
2.2.2
2.2.3
2.3
MOSFET and Diode Losses .........................................................................................................3
Conduction Losses..........................................................................................................................3
RDSon - Taking the Temperature and Production Variations into Account.......................................5
Switching Losses ............................................................................................................................6
Switch-on transient..........................................................................................................................6
Switch-off transient..........................................................................................................................9
Switching Energies and Losses ....................................................................................................10
Loss Balance.................................................................................................................................10
3
3.1
3.2
3.3
3.4
3.5
3.6
Application Specific Parameters ...............................................................................................11
Step-down (Buck) Converter.........................................................................................................11
Step-up (Boost) Converter ............................................................................................................12
DC Motor Drive..............................................................................................................................13
Three-Phase AC Motor Drive........................................................................................................16
Switched Reluctance Motor Drive .................................................................................................18
Piezo-Electric Actuator ..................................................................................................................19
4
Conclusion...................................................................................................................................20
5
Abbreviations ..............................................................................................................................21
Application Note
2
2006-07-31
MOSFET Converter Losses
1
Abstract
The aim of this Application Note is to provide a mathematical tool for the calculation of power losses in
MOSFET-based power electronics converters used in automotive applications. After a general discussion on
power losses calculation using the data-sheet parameters, the typical applications will be reviewed in order
to extract the application specific parameters important for the loss balance.
2
MOSFET and Diode Losses
Power losses (Pl) in any component operating in the switch-mode can be divided in three groups:
a) Conduction losses (Pc)
b) Switching losses (Psw)
c) Blocking (leakage) losses (Pb), normally being neglected
Therefore:
Pl = Pc + Psw + Pb ≈ Pc + Psw
2.1
Conduction Losses
Conduction losses in power MOSFET can be calculated using an MOSFET-approximation with the drainsource on-state resistance (RDSon):
u DS (iD ) = RDSon (iD ) ⋅ iD
uDS and iD are drain-source voltage and the drain current, respectively. The typical RDSon can be read from
the data-sheet diagram, as shown in Fig. 1, where ID is the MOSFET on-state current as defined by the
application.
Figure 1
Drain source resistance as a function of drain current (at TJ=25°C)
3
MOSFET Converter Losses
Therefore, the instantaneous value of the MOSFET conduction losses is:
pCM (t ) = u DS (t ) ⋅ i D (t ) = R DSon ⋅ i D2 (t )
Integration of the instantaneous power losses over the switching cycle gives an average value of the
MOSFET conduction losses:
PCM
1
=
Tsw
Tsw
1
∫0 pCM (t )dt = Tsw
Tsw
∫ (R
DSon
2
⋅ i D2 (t ))dt = RDSon ⋅ I Drms
0
where IDrms is the rms value of the MOSFET on-state current.
The conduction losses of the anti-parallel diode can be estimated using a diode approximation with a series
connection of DC voltage source (uD0) representing diode on-state zero-current voltage and a diode on-state
resistance (RD), uD being the voltage across the diode and iF the current through the diode:
u D (iD ) = u D 0 + RD ⋅ iF
These parameters can be read from the diagrams in the MOSFET datasheet as shown in fig. 2. In order to
take the parameter variation into account, and thus to have a conservative calculation, the uD0 value read
from the diagram have to be scaled with (uDmax/uDtyp). Those exact values can be read from the datasheet
tables, but for an engineering calculation a typical safety margin value of (10%-20%) can also be used.
Figure 2
Diode resistance as a function of the diode current
The instantaneous value of the diode conduction losses is:
pCD (t ) = u D (t ) ⋅ iF (t ) = u D 0 ⋅ iF (t ) + RD ⋅ iF2 (t )
If the average diode current is IFav, and the rms diode current is IFrms, the average diode conduction losses
across the switching period (Tsw=1/fsw) are:
PCD =
1
Tsw
Tsw
∫
0
pCD (t )dt =
1
Tsw
Tsw
∫ (u
D0
2
⋅ iF (t ) + RD ⋅ iF2 (t ))dt = u D 0 ⋅ I Fav + RD ⋅ I Frms
0
4
MOSFET Converter Losses
2.1.1
RDSon - Taking the Temperature and Production Variations into Account
The procedure for RDSon determination, shown in figure 1, refers to the RDSon typical values. While this
procedure should be satisfying for the majority of applications, the RDSon value can be calculated by taking
into account the temperature and production variations. It can be done using following equation:
α 

RDSon (TJ ) = RDSonMAX (25 C ) ⋅ 1 +

 100 
TJ − 25°C
o
where TJ is the junction temperature and RDSonMAX(25°C) is the maximum value of RDSon at 25°C, which can
be read from the product summary table in the data-sheet as shown in the fig. 3. The temperature coefficient
α can be calculated in the following manner: Two sets of values (TJ1, RDSon1) and (TJ2, RDSon2) can be read
from the data sheet as shown in fig. 4. These values can be used with the last equation to determine α.
Figure 3
Figure 4
Reading RDSonMAX(25°C) from the data-sheet
Reading TJ/RDSon from the data-sheet
5
MOSFET Converter Losses
2.2
Switching Losses
The circuit for the examination of the MOSFET switching losses is presented in fig. 5. It is a single-quadrant
chopper supplying an inductive type load. The MOSFET is driven from the driver circuit, providing a voltage
UDr at its output. The MOSFET internal diode is used as a free-wheeling diode, because in the majority of
applications, such as 3-phase AC motor drives, DC-motor drives, synchronous DC/DC converters, etc., the
power electronics converter consists of one or more MOSFET-based half-bridges. If an external freewheeling diode is used, the calculations are still valid, provided the diode parameters are taken from the
diode data-sheet.
Figure 5
MOSFET chopper with an inductive load
For the engineering calculations of the power loss balance, a linear approximation of the MOSFET switching
process is sufficient and, as will be shown later, presents the worst case calculation. The idealised switching
process of the power MOSFET is presented in Fig. 6. The uppermost part (A) presents the gate voltage (uGS)
and current (iG); the next one (B) shows the drain-source voltage (uDS) and the drain current (iD) without
taking the reverse recovery of the free-wheeling diode into account. The part C gives a qualitative overview
of the power losses, while the part D shows the reverse-recovery effects on the switching losses.
2.2.1
Switch-on transient
•
Driver circuit changes its state from 0V to UDr, the gate voltage rises to the threshold voltage (UGS(th)),
with the time-constant defined by the gate resistor and the equivalent MOSFET input capacitance
(Ciss=CGD+CGS). Until the gate voltage reaches the UGS(th), the output does not change.
•
After the UGS(th) has been reached, the drain current rises and takes over the load current. The worst
case value of the current rise-time (tri) between zero and IDon (defined by the application) can be
read from the MOSFET data-sheet, as shown in fig. 7. During the current rise-time, the free-wheeling
diode is still conducting and the drain-source voltage is UDD.
•
In order for the diode to switch off, all the minority carriers stored in it have to be removed (see fig.
6D). This reverse-recovery current has to be absorbed by the MOSFET, causing additional power
losses. The worst-case values of the reverse-recovery charge (Qrr) and duration (trr), which will be
used in the power loss calculation, can again be read from the MOSFET data-sheet (see fig. 8)
6
MOSFET Converter Losses
Figure 6
Switching transients of the power MOSFET
7
MOSFET Converter Losses
Figure 7
Figure 8
•
Reading the current rise- (red) and fall-time (blue) from the data-sheet
Reading the reverse recovery time (red) and charge (blue) from the data-sheet
After the diode has been switched off, the drain-source voltage is falling from uDS=UDD to its on-state
value uDS=RDSon·Ion. The Miller effect takes place and the gate-source voltage is clamped at the
uGS=U(plateau) (see fig. 9). The slope of the drain-source voltage is dictated through the gate current
flowing through the gate-drain capacitance (CGD=Crss). In order to calculate the voltage fall-time (tfu)
with a reasonable accuracy, the non-linearity of the gate-drain capacitance has to be taken into
account. The typical dependence of the gate-drain capacitance on the drain-source voltage is shown
in the fig. 10. Such non-linearity can not be easily incorporated into the engineering calculations.
That is why a two-point approximation is used. It is supposed that if the drain-source voltage is in the
range uDS∈[UDD/2,UDD], then the gate-drain capacitance takes value of CGD1= CGD(UDD). On the other
hand, if the drain-source voltage is in the range uDS∈[0V,UDD/2], then the gate-drain capacitance
takes value of CGD2= CGD(RDSon·Ion). The way to determine those capacitances is shown in fig. 10.
The drain-source voltage during the fall time, the two-point approximation being taken into account,
is shown in fig. 6B with the dotted line. Since this approximation is used only to determine the
voltage fall time (as well as the rise time during switch off) and the drain-source voltage is assumed
to have the linear form (solid line in fig. 6B), it becomes clear that this analysis presents the worstcase for the switching losses calculation.
The gate current during tfu can be calculated as:
I Gon =
U Dr − U ( plateau )
RG
The voltage fall time can now be calculated as a median of the fall times defined through the gate
current and the capacitances CGD1 and CGD2.
tfu =
tfu1 + tfu 2
2
where:
8
MOSFET Converter Losses
tfu1 = (U DD − RDSon ⋅ I Don )
CGD1
CGD1
= (U DD − RDSon ⋅ I Don ) ⋅ RG ⋅
I Gon
(U Dr − U ( plateau ) )
tfu 2 = (U DD − RDSon ⋅ I Don )
CGD 2
CGD 2
= (U DD − RDSon ⋅ I Don ) ⋅ RG ⋅
I Gon
(U Dr − U ( plateau ) )
Figure 9
Figure 10
2.2.2
Reading the plateau voltage from the data-sheet
Two-point representation of the gate-drain capacitance
Switch-off transient
Switch-off process corresponds to the switching-on process of the MOSFET in the reverse order and will
thus not be discussed in detail. Two important differences are:
•
No reverse recovery takes place
•
The gate current and the voltage rise time can be expressed as:
I Goff = −
U ( plateau )
RG
9
MOSFET Converter Losses
tru =
tru1 + tru 2
2
tru1 = (U DD − RDSon ⋅ I Don )
CGD1
CGD1
= (U DD − RDSon ⋅ I Don ) ⋅ RG ⋅
I Goff
U ( plateau )
tru 2 = (U DD − RDSon ⋅ I Don )
2.2.3
CGD 2
C
= (U DD − RDSon ⋅ I Don ) ⋅ RG ⋅ GD 2
I Goff
U ( plateau )
Switching Energies and Losses
According to previous considerations, the worst case turn-on energy losses in power MOSFET (EonM) can be
calculated as the sum of the switch-on energy without taking the reverse recovery process into account
(EonMi) and the switch-on energy caused by the reverse-recovery of the free-wheeling diode (EonMrr):
tri + tfu
∫u
EonM =
DS
(t ) ⋅ iD (t )dt = EonMi + EonMrr = U DD ⋅ I Don ⋅
0
tri + tfu
+ Qrr ⋅ U DD
2
The peak of the reverse-recovery current can be calculated as:
I Frrpeak =
2 ⋅ Qrr
trr
Turn-on energy in the diode consists mostly of the reverse-recovery energy (EonD):
tri +tfu
EonD =
∫u
D
(t ) ⋅ iF (t )dt ≈ EonDrr =
0
1
⋅ Qrr ⋅ U Drr
4
where UDrr is the voltage across the diode during reverse recovery. For the worst case calculation this
voltage can be approximated with a supply voltage (UDrr= UDD).
The switch-off energy losses in the MOSFET can be calculated in the similar manner. The switch-off losses
in the diode are normally neglected (EoffD≈0). Therefore:
tru +tfi
EoffM =
∫u
DS
(t ) ⋅ iD (t )dt = U DD ⋅ I Doff ⋅
0
tru + tfi
2
The switching losses in the MOSFET and the diode are the product of switching energies and the switching
frequency (fsw):
PswM = ( EonM + EoffM ) ⋅ f sw
PswD = ( EonD + EoffD ) ⋅ f sw ≈ EonD ⋅ f sw
2.3
Loss Balance
Power losses in the MOSFET and the free-wheeling diode can be expressed as the sum of the conduction
and switching losses giving:
2
PM = PCM + PswM = RDSon ⋅ I Drms
+ ( EonM + EoffM ) ⋅ f sw
2
PD = PCD + PswD = u D 0 ⋅ I Fav + RD ⋅ I Frms
+ EonD ⋅ f sw
10
MOSFET Converter Losses
3
Application Specific Parameters
In the following text the typical applications will be revisited together with the typical signal waveforms
necessary for the power loss balance calculation.
3.1
Step-down (Buck) Converter
Figures 11 and 12 present the topology and the typical signals in the step-down (buck) converter.
Figure 11
Figure 12
Step-down converter topology
Step-down converter – typical signals
Input parameters for the calculation: Input voltage (Uin), output voltage (Uo), output power (Po), inductor value
(L), switching frequency (fsw).
Output current:
Io =
Po
Uo
Duty cycle in continuous conduction mode:
D=
Uo
U in
Output current ripple:
11
MOSFET Converter Losses
∆I o =
(1 − D)U o
L ⋅ f sw
The parameters needed for the loss calculation can be determined according to previously calculated values
as:
I Don = I o −
∆I o
2
I Doff = I o +
∆I o
2
2
I Drms
= D ⋅ I o2 = ( D ⋅ I o ) 2
I Fav = (1 − D) ⋅ I o
2
I Frms
= (1 − D) ⋅ I o2 = ( 1 − D ⋅ I o ) 2
3.2
Step-up (Boost) Converter
Figures 13 and 14 present the topology and the typical signals in the step-up (boost) converter.
Figure 13
Figure 14
Step-up converter topology
Step-up converter – typical signals
12
MOSFET Converter Losses
Input parameters for the calculation: Input voltage (Uin), output voltage (Uo), output power (Po), input power
(Pin), inductor value (L), switching frequency (fsw).
Input current:
I in =
Pin
U in
Duty cycle in continuous conduction mode:
D =1−
U in
Uo
Input current ripple:
∆I in =
D ⋅ U in
L ⋅ f sw
The parameters needed for the loss calculation can be determined according to previously calculated values
as:
I Don = I in −
∆I in
2
I Doff = I in +
∆I in
2
2
I Drms
= D ⋅ I in2 = ( D ⋅ I in ) 2
I Fav = (1 − D) ⋅ I in
2
I Frms
= (1 − D) ⋅ I in2 = ( 1 − D ⋅ I in ) 2
3.3
DC Motor Drive
Figures 15 and 16 present the topology and the typical signals in the single-quadrant chopper for the DC
motor drive.
Figure 15
Single-quadrant DC motor drive
13
MOSFET Converter Losses
Figure 16
Single-quadrant DC motor drive – typical signals
Input parameters for the calculation: Input voltage (UDD), output voltage (Uo), output power (Po), armature
inductor value (L), armature resistance value (R), motor back-emf value (E), switching frequency (fsw).
Average value of the output current:
Io =
Po
Uo
Duty cycle in continuous conduction mode:
D=
Uo
U DD
Minimum output current:
I o min =

 D

L

 fsw⋅
R

U DD 1 − e

R

1− e










−

1 
L
fsw 
R
E
R
Maximum output current:
I o max =


− D
L

 fsw⋅
R

U DD 1 − e

R

1− e








− 1 
L

 fsw 

R
−
E
R
Output current ripple:
∆I o = I o max − I o min
The parameters needed for the loss calculation can be determined according to previously calculated values
as:
I Don = I o −
∆I o
2
14
MOSFET Converter Losses
I Doff = I o +
∆I o
2
2
I Drms
= D ⋅ I o2 = ( D ⋅ I o ) 2
I Fav = (1 − D) ⋅ I o
2
I Frms
= (1 − D) ⋅ I o2 = ( 1 − D ⋅ I o ) 2
Figures 17…18 present the topology and the typical signals in the four-quadrant chopper for the DC motor
drive. Fig. 18 shows the case of the bipolar PWM, while the fig. 19 shows the case of the unipolar PWM.
Appropriate values can be determined following the same procedure as for the single-quadrant chopper,
taking into account that for the bipolar PWM the voltage excursion on the load is 2UDD.
Figure 17
Figure 18
Four-quadrant DC motor drive
Four-quadrant DC motor drive – typical signals with bipolar PWM
15
MOSFET Converter Losses
Figure 19
3.4
Four-quadrant DC motor drive – typical signals with unipolar PWM
Three-Phase AC Motor Drive
Figures 19 and 20 present the topology and the typical signals in the three-phase inverter for the AC motor
(permanent magnet synchronous, brushless DC, induction motor) drive. Typical applications are: electric
power steering (EPS), Starter-Generator (Alternator), fans, blowers, HVAC etc.
Figure 20
Three-phase AC motor drive
Input parameters for the calculation: Input voltage (UDD), output line-to-line voltage (Uo) or output phase
voltage (Uan1), rms value of the output current (Iorms) or output apparent power (So=3Uan1Iorms), motor
displacement factor (cosφ1), equivalent stator inductance (L), switching frequency (fsw), output (motor
electrical) frequency fo and an inverter amplitude modulation index ma
Output current ripple:
∆I a =
(U DD − 2 ⋅ U o ) ⋅ U o
2 ⋅ L ⋅ U DD ⋅ f sw
Peak value of the output current:
I o = 2 ⋅ I orms
16
MOSFET Converter Losses
MOSFET conduction losses:
1 m ⋅ cos φ1
2
)
PCM = RDSon ⋅ I Drms
= RDSon ⋅ I o2 ⋅ ( + a
8
3 ⋅π
Diode Conduction losses:
2
PCD = u D 0 ⋅ I Fav + RD ⋅ I Frms
= uD0 ⋅ I o ⋅ (
m ⋅ cos φ1
1
1 m ⋅ cos φ1
) + RD ⋅ I o2 ⋅ ( − a
)
− a
2 ⋅π
8
8
3 ⋅π
In order to find a simple solution for the switching loss calculation, it is supposed that the losses generated in
the inverter in one half-wave of the output frequency (1/(2 fo) ) correspond to the losses generated if instead
of AC output current a DC equivalent output current is applied. The equivalent DC output current value is:
I DC =
1
π
⋅ Io
This value can be used for [IDon, IDoff] in the switching loss calculation as described in detail in the chapter 2.3.
Figure 21
Three-phase AC motor drive – typical signals
17
MOSFET Converter Losses
3.5
Switched Reluctance Motor Drive
Figures 22, 23 and 24 present the topology and the typical signals in the two-quadrant chopper for one
phase of the switched reluctance motor drive. The complete converter consists of more two-quadrant
converters, the number of which depends on the number of the motor phases. The procedure for the power
loss calculation is practically the same as with the DC motor drive and therefore the same equations can be
used.
Figure 22
Two-quadrant converter for one phase winding of the switched reluctance motor drive
Figure 23
Switched reluctance motor drive – typical signals with bipolar PWM
18
MOSFET Converter Losses
Figure 24
3.6
Switched reluctance motor drive – typical signals with unipolar PWM
Piezo-Electric Actuator
Figures 25 and 26 present the topology and the typical signals in the two-quadrant DC/DC converter for the
piezo-electric actuator, used, for example, in direct injection systems. The procedure for the power loss
calculation is the same as with the step-down (buck) converter during charging and the same as with the
step-up (boost) converter during the discharging. Namely, while the actuator is charging, the system behaves
like a step-down converter (MOSFET 1 and Diode 2 are active) and the energy flows from UDD to CA and the
energy flow reverses while the CA is discharging (MOSFET 2 and Diode 1 are active).
Figure 25
Two-quadrant converter for piezo-electric actuator
19
MOSFET Converter Losses
Figure 26
4
Converter for piezo-electric actuator – typical signals
Conclusion
This Application Note presented a mathematical tool for the calculation of power losses in MOSFET-based
power electronics converters used in automotive applications. Mathematical model for the power loss
balance calculation using the data-sheet parameters was presented. The typical automotive applications
were reviewed and the application specific parameters important for the loss balance were extracted.
20
MOSFET Converter Losses
5
Abbreviations
Pl
Power losses
Pc
Conduction losses
Psw
Switching losses
Pb
Blocking (leakage) losses
pCM
Instantaneous value of the MOSFET conduction losses
PCM
Average value of the MOSFET conduction losses
pCD
Instantaneous value of the diode conduction losses
PCM
Average value of the diode conduction losses
PswM
MOSFET switching losses
PswD
Diode switching losses
PM
MOSFET losses
PD
Diode losses
Po
Converter output power
EonM
MOSFET switch-on energy
EonMi
MOSFET switch-on energy without taking the reverse recovery process into account
EonMrr
MOSFET switch-on energy caused by the reverse-recovery of the free-wheeling diode
EonD
Diode energy during MOSFET switch-on transient
EoffM
MOSFET switch-off energy
uDS
Drain-source voltage
uD
Voltage across the diode
uD0
Diode on-state zero-current voltage
UDr
Driver output voltage
UGS
Gate-source voltage
UGSth
Gate-source threshold voltage
U(plateau) Plateau voltage
UDrr
Voltage across the diode during reverse recovery
UDD
Converter supply (DC bus) voltage
Uin
Converter input voltage
Uo
Converter output voltage
uL
Voltage across the load
iD
Drain current
IDrms
RMS value of the drain current
iF
Current through the diode
IFav
Average diode current
IFrms
RMS value of the diode current
Irr
Reverse recovery current
IFrrpeak
Peak value of the diode reverse recovery current
21
MOSFET Converter Losses
IG
Gate current
iL
Load current
Iin
Converter input current
Io
Converter output current
RDSon
Drain source on-state resistance
RD
Diode on-state resistance
RG
Gate resistor
CGS
Gate-source capacitance
CGD
Gate-drain capacitance
CDS
Drain-source capacitance
Qrr
Reverse recovery charge
R
Load resistor
L
Load Inductance
Tj
Junction temperature
α
Temperature coefficient
Tsw
Switching period
fsw
Switching frequency
tri
Current rise time
tfi
Current fall time
tru
Voltage rise time
tfu
Voltage fall time
trr
Reverse recovery time
D
Duty cycle
22
Edition 2006-07-31
Published by Infineon Technologies AG,
Am Campeon 1-12,
85579 Neubiberg, Germany
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